Kinematics of Machines.
485
Revolutions of mandrel _ No. of threads perjnch. on mandrel
Revolutions of leadingscrew ~ No. of threads per iF. oiileadingscSrew
in order to cut a definite pitch. This may also be stated as
followers at L. S.jsnd _ pitch L. S.
drivers at M end ~~ pitch M screw
or the pitches and wheels are in the same ratio^ which ratio, being
found, must be accommodated by a suitable train.
Example 46. — In Plate V., the leading screw being. £" pitch, and
the wheels in the set rising by 5 at a time from 20 to 120 teeth, it is
required to arrange wheels to cut (i) a screw of ro threads per inch,
righthanded, and (2) a screw of L" pitch lefthanded.
Pitch ratio

Putting 30 teeth on n (Fig. 135) into 75 on stud (£, Fig. 140): 30
teeth on stud into 90 on L.S., we have,
75 x 9° ^ i§ and the handle at n
must be down.
wheel ratio =
(2) pitch ratio
30 x 30
*±§  1
M"" ~ i =
Putting 45 teeth on L.S. and 60 teeth on n; with any intermediate
on stud (say 60) we have,
wheel ratio  11 _ 3 and the h^nd1^ at n must
 60 4 btup.
Kinematics (of Machines) is a method of attacking
machine problems devised by Prof. Reuleaux, and anglicised by
Prof. Kennedy. We shall proceed to discuss its principles.
Pairs.—The constraining parts are termed pairs because
they always occur in sets of two. Of these there are higher and
lower pairs. The former connect by points or lines, but the
latter by their whole surfaces.
Three kinds of lower pairs are possible: I. Sliding pairs,
as a piston and cylinder. II. Turning pairs, as a journal or pin.
III. Screw pairs, including all screws and nuts. Complete or
dosed pairs have their motions fully defined: incomplete pairs
require further closure, as at Fig. 444, where gravity is not for
the moment considered.